Problem 7-19 (Algo) A cafeteria serving line has a coffee urnfrom which customers serve themselves. Arrivals at the urn follow aPoisson distribution at the rate of 2.5 per minute. In servingthemselves, customers take about 16 seconds, exponentiallydistributed.

a. How many customers would you expect to see, on average, atthe coffee urn? (Do not round intermediate calculations. Round youranswer to 2 decimal places.)

b. How long would you expect it to take to get a cup of coffee?(Round your answer to 2 decimal places.)

c. What percentage of time is the urn being used? (Do not roundintermediate calculations. Round your answer to 1 decimalplace.)

d. What is the probability that three or more people are in thecafeteria? (Do not round intermediate calculations. Round youranswer to 1 decimal place.)

e. If the cafeteria installs an automatic vendor that dispensesa cup of coffee at a constant time of 16 seconds, how manycustomers would you expect to see at the coffee urn (waiting and/orpouring coffee)? (Do not round intermediate calculations. Roundyour answer to 2 decimal places.)

f. If the cafeteria installs an automatic vendor that dispensesa cup of coffee at a constant time of 16 seconds, how long wouldyou expect it to take (in minutes) to get a cup of coffee,including waiting time? (Do not round intermediate calculations.Round your answer to 2 decimal places.)